I am trying to find the probability for a Poisson distribution. The mean is two cars sold per day. The question is:
"What is the probability that at least one car is sold for each of three consecutive days?"
I know that the probability of at least one car being sold for $1$ day is:
$P$($X$ $≤$ $1$) $ =$ $P$($X = 1$) + $P$($X = 0$) = $0.135335283 + 0.270670566$ = $0.406005849$
But the part that throws me off is the term "for EACH of three consecutive days". If the question was "find the probability of at least one car being sold for three days", all I would have to do it multiply the mean ($2$ cars) by $3$ days and the final answer would be $0.017351265$.
But since when the question says "for EACH of three consecutive days", does it mean I take the probability of at least one car sold in 1 day, and multiply it by itself for each of the three days? That is: $0.406005849$ to the power of $3$ = $.066926308$.
I just want to know what is the correct way to calculate it by "each consecutive day." Should the answer be $0.017351265$ or $.066926308$. Any help would be appreciated.